Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?

Rune Johansen

Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?

Dynamical Systems 2013-04-04 v1

Authors: Rune Johansen

Abstract

Is every irreducible shift of finite type flow equivalent to a renewal system? For the first time, this variation of a classic problem formulated by Adler is investigated, and several partial results are obtained in an attempt to find the range of the Bowen--Franks invariant over the set of renewal systems of finite type. In particular, it is shown that the Bowen--Franks group is cyclic for every member of a class of renewal systems known to attain all entropies realised by shifts of finite type, and several classes of renewal systems with non--trivial values of the invariant are constructed.

Keywords

shift of finite type renewal system flow equivalence Bowen--Franks invariant Bowen--Franks group topological entropy symbolic dynamics

Cite

@article{arxiv.1304.0888,
  title  = {Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?},
  author = {Rune Johansen},
  journal= {arXiv preprint arXiv:1304.0888},
  year   = {2013}
}

Comments

22 pages, 5 figures. For the conference proceedings of Operator Algebra and Dynamics, NordForsk Network Closing Conference, 15-20 May 2012, Gj\'aargar{\eth}ur, Faroe Islands

Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?

Abstract

Keywords

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